1. Technical Field
The present invention relates to prevent a lowering of Q value due to thermal conduction, particularly of a resonator element and an oscillator.
2. Related Art
Tuning fork type piezoelectric resonator elements have been widely used. In such tuning fork type piezoelectric resonator element, a pair of resonating arms vibrates to be closer to each other and apart from each other. Vibration energy losses generated in the flexural vibration of the tuning fork type resonator element cause a resonator to deteriorate the performances. For example, an increase of a CI (crystal impedance) value or a decrease of a Q value occurs. Thermal conduction is considered as one factor of the vibration energy losses.
FIG. 7 is an explanatory view of the thermal conduction of a piezoelectric resonator element. As shown in FIG. 7, a piezoelectric resonator element 1 includes two resonating arms 3 and 4 extending from a connecting section 2 in parallel. When a predetermined voltage is applied to exciting electrodes (not shown) in this state, the resonating arms 3 and 4 vibrate. In a vibration state in which the resonating arms 3 and 4 vibrate to be apart from each other, a compression stress is applied around root portions shown as shaded regions A at the outsides of the resonating arms 3 and 4. In contrast, an extension stress is applied around root portions shown as shaded regions B at the inner sides of the resonating arms 3 and 4.
In a vibration state in which the resonating arms 3 and 4 vibrate to be closer to each other, an extension stress is applied to the shaded regions A while a compression stress is applied to the shaded regions B. In the regions to which the compression stress is applied, the temperature increases while in the regions to which the extension stress is applied, the temperature decreases. The thermal conduction generated between the compression portions receiving the compression stress and the extension portions receiving the extension stress of the resonating arms that vibrate in a flexural mode causes the vibration energy losses. Lowering of the Q value caused by the thermal conduction is called a thermoelastic loss.
In order to prevent or suppress the lowering of the Q value due to the thermoelastic loss, a tuning fork type resonator is disclosed that includes vibrating arms each having a rectangular section and a groove or a hole formed on the centerline thereof, in JP-UM-A-2-32229, for example.
The JP-UM-A-2-32229 describes that the Q value, which shows the thermoelastic loss, becomes minimum at fm=½π·τ where fm is a relaxation frequency, and τ is a relaxation time, in a resonator vibrating in a flexural mode. This is derived from a stress-strain relation equation that is well known in a case of internal friction, which is generally caused by temperature difference, of a solid. The relation of the Q value and the frequency is generally shown as a curve F in FIG. 8. In the figure, a frequency at which the Q value is a minimum Q0 is a thermal relaxation frequency f0(=½π·τ). A region of higher frequency (1<f/f0) is referred to as an adiabatic region while a region of lower frequency (f/f0<1) is referred to as an isothermal region where “f/f0=1” is a reference point.
Incidentally, a flexural resonator element is disclosed, for example, in JP-A-2005-39767 as a tuning fork type flexural resonator having a frequency of a fundamental mode vibration with high frequency stability, and a high Q value. FIGS. 9A and 9B show schematic structures of the flexural resonator element in related art. FIG. 9A is a plan view. FIG. 9B is a cross sectional view taken along the line A-A of FIG. 9A. A flexural resonator element 100 includes tuning fork arms 102 and a tuning fork arm base section 104. The tuning fork arm 102 has grooves 106 at the upper and lower surfaces. Electrodes 110 and 112 are provided to the side surfaces of the grooves 106. Electrodes 114 and 116 having different polarities are provided to the side surfaces of the tuning fork arms 102. The electrodes provided the side surfaces of the grooves are faced to each other with the piezoelectric body interposed therebetween, and likewise the electrodes provided to the side surfaces of the tuning fork arms are faced to each other with the piezoelectric body interposed therebetween.
In the structure disclosed in the JP-A-2005-39767, a heat transfer path between a compression region and an extension region of the tuning fork arms 102 is narrowed by the grooves 106 on the way as shown in FIG. 9B. As a result, a relaxation time τ, which is a period during which the temperatures of the compression region and the extension region come to an equilibrium state, lengthens. As can be seen in an adiabatic region of FIG. 8, the curve F is shifted to a position of a curve F1 in a lower frequency side as a result of forming the grooves 106. In this shift, the relaxation frequency is lowered and the shape of the curve F is not changed. Accordingly, the Q value increases as shown with an arrow “a”. On the other hand, the curve F is shifted to a position of a curve F2 when electrodes are formed. The Q value decreases as shown with an arrow “b”. The reason of the shift can be considered that the electrodes form a heat transfer path. A material having conductive property, such as an electrode material, has large thermal conductivity. In the conductive material, thermal energy is carried by electrons in addition to phonons of metal. As shown in FIG. 9B, thermal conduction is achieved through the electrodes in addition to the material, i.e., quartz crystal, shortening the relaxation time τ to increase the relaxation frequency. As a result, it can be considered that the curve F is shifted to the position of the curve F2 in a higher frequency side.